One-loop black-hole matching for finite quantum Love numbers

Determine the finite values of the scalar and electromagnetic Love numbers at a reference renormalization scale by matching the worldline effective theory to a one-loop computation in a Schwarzschild black-hole background.

Background

The paper computes the ultraviolet divergences and renormalization-group beta functions of the leading scalar and electromagnetic Love-number operators for a Schwarzschild black hole. These beta functions determine the logarithmic scale dependence of the Love numbers, but they do not fix their finite values at any particular reference scale.

Fixing those finite matching constants requires a one-loop calculation performed directly in the black-hole background and matching its result to the worldline effective field theory. The paper explicitly leaves this calculation unresolved; without it, the absolute finite Love numbers remain undetermined even though their quantum running is known.